Abstract
In order to classify and understand structure of the spacetime, investigation of the geodesic motions of massive and massless particles is a key tool. So the geodesic equation is a central equation of gravitating systems and the subject of geodesics in the black hole dictionary attracted much attention. In this paper, we give a full description of geodesic motions in three-dimensional spacetime. We investigate the geodesics near charged BTZ black holes and then generalize our prescriptions to the case of massive gravity. We show that electric charge is a critical parameter for categorizing the geodesic motions of both lightlike and timelike particles. In addition, we classify the type of geodesics based on the particle properties and geometry of spacetime.
Highlights
One of the predictions of general relativity (GR) is the existence of black holes
We investigate the geodesics near charged BTZ black holes and generalize our prescriptions to the case of massive gravity
We show that electric charge is a critical parameter for categorizing the geodesic motions of both lightlike and timelike particles
Summary
One of the predictions of GR is the existence of black holes. These mysterious singular solutions can be described by the first static spherically symmetric solution of Einstein’s field equations found by Karl Schwarzschild in 1916. A first seminal paper for studying the geodesic equations and its analytical solutions was by Hagihara in 1931, when he solved the geodesic equations of Schwarzschild black holes in terms of Weierstrass elliptic functions [97]. Regarding three dimensional spacetime, the stability and existence of circular geodesics in a family of asymptotically AdS black holes in new massive gravity theory [121] and the null geodesics in a static circularly symmetric black hole spacetime [122] have been investigated before. We present the geodesic equation and effective potential in BTZ and its extension to massive gravity black holes, and define acceptable regions of motion. 3. we completely classify geodesic motions and solve the geodesic equation around the (charged) BTZ black holes in Sect.
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